MATH5975代写、代写python,c++编程

日期：2023-03-05 11:17

Introduction to Stochastic Analysis

Term 1, 2023

Cricos Provider Code: 00098G

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Staff

Position Name Email Room

Lecturer-in-charge Dr Libo Li libo.li@unsw.edu.au RC-1035

Please refer to your Timetable on MyUNSW for your Lecture Tut, Lab enrolment days and times.

Timetable weblink: http://timetable.unsw.edu.au/2023/MATH5975.html

Administrative Contacts

Please visit the School of Mathematics and Statistics website for a range of information on School

Policies, Forms and Help for Students.

For information on Courses, please go to “Current Students” and either Undergraduate and/or

Postgraduate”, Course Homepage” for information on all course offerings,

The “Student Notice Board” can be located by going to the “Current Students” page; Notices are

posted regularly for your information here. Please familiarise yourself with the information found

in these locations. The School web page is: https://www.maths.unsw.edu.au

If you cannot find the answer to your queries on the web you are welcome to contact the Student

Services Office directly.

By email Postgraduate pg.mathsstats@unsw.edu.au

By phone: 9385 7053

Should we need to contact you, we will use your official UNSW email address of in the first

instance. It is your responsibility to regularly check your university email account. Please state

your student number in all emails.

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Course Information

Course Aims

Modern theory of financial markets relies on advanced mathematical and statistical methods that

are used to model, forecast and manage risk in complex financial transactions. After the

publication in 1973 of the ground-breaking paper of Black and Scholes on the arbitrage pricing of

European call options, it became clear that Stochastic Analysis is an indispensable tool for the

theory of financial markets, derivation of prices of standard and exotic options and other derivative

securities, hedging related financial risk, as well as managing the interest rate risk.

In this course, you will learn the basic concepts and techniques of Stochastic Analysis, such as:

Brownian motion, martingales, Ito stochastic integral, Ito's formula, stochastic differential

equations, equivalent change of a probability measure, integral representation of martingales with

respect to a Brownian filtration, relations to second order partial differential equations, the

Feynman-Kac formula, and stochastic processes with discontinuities.

The course consists of theorems and proofs. The main goal of the course is to provide a

necessary mathematical background for MATH5816 Continuous Time Financial Modelling and

MATH5985 Term Structure Modelling, rather than to focus directly on financial concepts.

Course Description

Modern theory of financial markets relies on advanced mathematical statistical methods that are

used to model, forecast and manage risk in complex financial transactions. After publication in

1973 of the ground-breaking paper of Black and Scholes on the arbitrage pricing of European call

options, Stochastic Analysis became an indispensable tool for the theory of financial markets,

derivation of prices of standard and exotic options and other derivative securities, hedging related

financial risk, as well as managing the interest rate risk. In this course, you will learn the basic

concepts and techniques of Stochastic Analysis, such as: Brownian motion, Ito stochastic integral,

Ito's formula, changes of measures, stochastic differential equations, and their relations to second

order partial differential equations, and Feynman-Kac formula.

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Assessment and Deadlines

Assessment Week Weighting

%

Due date if applicable Course Learning

Outcome (CLO)

Assignment 1 Week 4 5% Due week 4 CLO1, CLO2, CL03

Midterm Test Week 7 20% Due week 7 CLO1, CLO2, CLO3

Assignment 2 Week 10 15% Due week 10 CLO1, CLO2, CLO3

Final Exam 60% UNSW Exam Period All

Late Submission of Assessment Tasks

No late submissions will be accepted. (Where "late" in this context means after any extensions

granted for Special Consideration or Equitable Learning Provisions.)

Course Learning Outcomes (CLO)

1. Recognise which analysis procedure is appropriate for a given research problem.

2. Apply probability theory and stochastic analysis to practical problems.

3. Demonstrate an understanding of the usefulness of Stochastic Analysis in your

professional area.

Course Schedule

The course will include material taken from some of the following topics. This is should only serve

as a guide as it is not an extensive list of the material to be covered and the timings are

approximate. The course content is ultimately defined by the material covered in lectures; refer to

Moodle for Lecture notes.

Weeks Topic

1 Basic Probability, Conditional Expectation

2 Stopping Times, Discrete Time Martingales

3 Continuous Time Martingale, Brownian Motion,

4 Stochastic Integrals

5 Ito's Formula

7 Continuous Semimartingales

8 Stochastic Differential Equation

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9 Radon Nikodym Density and Girsanov Theorem

10 Feynman-Kac Formula

Moodle

Log in to Moodle to find announcements, general information, notes, lecture slide, classroom

tutorial and assessments etc.

https://moodle.telt.unsw.edu.au

School and UNSW Policies

The School of Mathematics and Statistics has adopted a number of policies relating to enrolment,

attendance, assessment, plagiarism, cheating, special consideration etc. These are in addition to

the Policies of The University of New South Wales. Individual courses may also adopt other

policies in addition to or replacing some of the School ones. These will be clearly notified in the

Course Initial Handout and on the Course Home Pages on the Maths Stats web site.

Students in courses run by the School of Mathematics and Statistics should be aware of the School

and Course policies by reading the appropriate pages on the Maths Stats web site starting at:

https://www.maths.unsw.edu.au/currentstudents/assessment-policies

The School of Mathematics and Statistics will assume that all its students have read and

understood the School policies on the above pages and any individual course policies on the

Course Initial Handout and Course Home Page. Lack of knowledge about a policy will not be an

excuse for failing to follow the procedure in it.

Academic Integrity and Plagiarism

UNSW has an ongoing commitment to fostering a culture of learning informed by academic

integrity. All UNSW staff and students have a responsibility to adhere to this principle of academic

integrity. Plagiarism undermines academic integrity and is not tolerated at UNSW. Plagiarism at

UNSW is defined as using the words or ideas of others and passing them off as your own.

The UNSW Student Code provides a framework for the standard of conduct expected of UNSW

students with respect to their academic integrity and behaviour. It outlines the primary

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obligations of students and directs staff and students to the Code and related procedures.

In addition, it is important that students understand that it is not permissible to buy

essay/writing services from third parties as the use of such services constitutes plagiarism

because it involves using the words or ideas of others and passing them off as your own. Nor is

it permissible to sell copies of lecture or tutorial notes as students do not own the rights to this

intellectual property.

If a student breaches the Student Code with respect to academic integrity, the University may take

disciplinary action under the Student Misconduct Procedure.

The UNSW Student Code and the Student Misconduct Procedure can be found at:

https://student.unsw.edu.au/plagiarism

An online Module “Working with Academic Integrity” (https://student.unsw.edu.au/aim) is a six-

lesson interactive self-paced Moodle module exploring and explaining all of these terms and

placing them into your learning context. It will be the best one-hour investment you’ve ever made.

Plagiarism

Plagiarism is presenting another person's work or ideas as your own. Plagiarism is a serious

breach of ethics at UNSW and is not taken lightly. So how do you avoid it? A one-minute video for

an overview of how you can avoid plagiarism can be found

https://student.unsw.edu.au/plagiarism.

Additional Support

ELISE (Enabling Library and Information Skills for Everyone)

ELISE is designed to introduce new students to studying at UNSW.

Completing the ELISE tutorial and quiz will enable you to:

analyse topics, plan responses and organise research for academic writing and other

assessment tasks

effectively and efficiently find appropriate information sources and evaluate relevance

to your needs

use and manage information effectively to accomplish a specific purpose

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better manage your time

understand your rights and responsibilities as a student at UNSW

be aware of plagiarism, copyright, UNSW Student Code of Conduct and Acceptable Use of

UNSW ICT Resources Policy

be aware of the standards of behaviour expected of everyone in the UNSW community

locate services and information about UNSW and UNSW Library

Some of these areas will be familiar to you, others will be new. Gaining a solid understanding of all

the related aspects of ELISE will help you make the most of your studies at UNSW.

The ELISE training webpages:

https://subjectguides.library.unsw.edu.au/elise/aboutelise

Equitable Learning Services (ELS)

If you suffer from a chronic or ongoing illness that has, or is likely to, put you at a serious

disadvantage, then you should contact the Equitable Learning Services (previously known as

SEADU) who provide confidential support and advice.

They assist students:

living with disabilities

with long- or short-term health concerns and/or mental health issues

who are primary carers

from low SES backgrounds

of diverse genders, sexes and sexualities

from refugee and refugee-like backgrounds

from rural and remote backgrounds

who are the first in their family to undertake a bachelor-level degree.

Their web site is: https://student.unsw.edu.au/els/services

Equitable Learning Services (ELS) may determine that your condition requires special

arrangements for assessment tasks. Once the School has been notified of these, we will make

every effort to meet the arrangements specified by ELS.

Additionally, if you have suffered significant misadventure that affects your ability to complete the

course, please contact your Lecturer-in-charge in the first instance.

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Academic Skills Support and the Learning Centre

The Learning Centre offers academic support programs to all students at UNSW Australia. We

assist students to develop approaches to learning that will enable them to succeed in their

academic study. For further information on these programs please go to:

http://www.lc.unsw.edu.au/services-programs

Applications for Special Consideration for Missed Assessment

Please adhere to the Special Consideration Policy and Procedures provided on the web page

below when applying for special consideration.

https://student.unsw.edu.au/special-consideration

Please note that the application is not considered by the Course Authority, it is considered by a

centralised team of staff at the Nucleus Student Hub.

The School will contact you (via student email account) after special consideration has been

granted to reschedule your missed assessment, for a lab test or paper-based test only.

For applications for special consideration for assignment extensions, please note that the new

submission date and/or outcome will be communicated through the special consideration web

site only, no communication will be received from the School.

For Dates on Final Term Exams and Supplementary Exams please check the “Key Dates for

Exams” ahead of time to avoid booking holidays or work obligations.

https://student.unsw.edu.au/exam-dates

If you believe your application for Special Consideration has not been processed, you should email

specialconsideration@unsw.edu.au immediately for advice.

Course Evaluation and Development (MyExperience)

Student feedback is very important to continual course improvement. This is demonstrated within

the School of Mathematics and Statistics by the implementation of the UNSW online student

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survey myExperience, which allows students to evaluate their learning experiences in an

anonymous way. myExperience survey reports are produced for each survey. They are released to

staff after all student assessment results are finalised and released to students. Course

convenor will use the feedback to make ongoing improvements to the course.